Related papers: First-Order Conditional Logic Revisited
In this paper we adapt the definitions and results from Apt and Vermeulen on `First order logic as a constraint programming language' (in: Proceedings of LPAR2001, Baaz and Voronkov (eds.), Springer LNAI 2514) to include important ideas…
We prove that the first-order logic of CZF is intuitionistic first-order logic. To do so, we introduce a new model of transfinite computation (Set Register Machines) and combine the resulting notion of realisability with Beth semantics. On…
We introduce and investigate here a formalisation for conditionals that allows the definition of a broad class of reasoning systems. This framework covers the most popular kinds of conditional reasoning in logic-based KR: the semantics we…
Description logics are a powerful tool for describing ontological knowledge bases. That is, they give a factual account of the world in terms of individuals, concepts and relations. In the presence of uncertainty, such factual accounts are…
Within classical propositional logic, assigning probabilities to formulas is shown to be equivalent to assigning probabilities to valuations. A novel notion of probabilistic entailment enjoying desirable properties of logical consequence is…
Default logic can be regarded as a mechanism to represent families of belief sets of a reasoning agent. As such, it is inherently second-order. In this paper, we study the problem of representability of a family of theories as the set of…
We consider the first-order theory of random variables with the probabilistic independence relation, which concerns statements consisting of random variables, the probabilistic independence symbol, logical operators, and existential and…
The purpose of this paper is to introduce justification logics based on conditional logics. We introduce a new family of logics, called conditional justification logics, which incorporates a counterfactual conditional in its language. For…
We analyze selected iterated conditionals in the framework of conditional random quantities. We point out that it is instructive to examine Lewis's triviality result, which shows the conditions a conditional must satisfy for its probability…
Fuzziness and randomicity widespread exist in natural science, engineering, technology and social science. The purpose of this paper is to present a new logic - uncertain propositional logic which can deal with both fuzziness by taking…
In response to a concern raised by Horty, this paper develops a two-tiered, preference-based semantic framework for modeling defeasible conditional obligations. The paper extends a Hansson-Lewis style preference semantics for dyadic deontic…
We introduce a natural Turing-complete extension of first-order logic FO. The extension adds two novel features to FO. The first one of these is the capacity to add new points to models and new tuples to relations. The second one is the…
In this thesis, we present two approaches to a rigorous mathematical and algorithmic foundation of quantitative and statistical inference in constraint-based natural language processing. The first approach, called quantitative constraint…
Substructural logics are formal logical systems that omit familiar structural rules of classical and intuitionistic logic such as contraction, weakening, exchange (commutativity), and associativity. This leads to a resource-sensitive…
The one-variable fragment of a first-order logic may be viewed as an "S5-like" modal logic, where the universal and existential quantifiers are replaced by box and diamond modalities, respectively. Axiomatizations of these modal logics have…
First-order logic has been established as an important tool for modeling and verifying intricate systems such as distributed protocols and concurrent systems. These systems are parametric in the number of nodes in the network or the number…
Argumentation problems are concerned with determining the acceptability of a set of arguments from their relational structure. When the available information is uncertain, probabilistic argumentation frameworks provide modelling tools to…
Type-free systems of logic are designed to consistently handle significant instances of self-reference. Some consistent type-free systems also have the feature of allowing the sort of general abstraction or comprehension principle that…
Large Language Models (LLMs) still struggle with complex logical reasoning. While previous works achieve remarkable improvements, their performance is highly dependent on the correctness of translating natural language (NL) problems into a…
Nested words are a structured model of execution paths in procedural programs, reflecting their call and return nesting structure. Finite nested words also capture the structure of parse trees and other tree-structured data, such as XML. We…